MATLAB: Does periodogram varies with data length

periodogrampsd

Hello,
I'm trying to understand better how periodogram works by using it with pure sinusoids.
Fs = 1000;
t = 0:1/Fs:1-1/Fs;
x = sin(2*pi*100*t);
[psdestx,Fxx] = periodogram(x,[],length(x),Fs);
plot(Fxx,psdestx); grid on;
xlabel('Hz');
title('Periodogram Power Spectral Density Estimate');
I took most of the above code from a MATLAB example in the documentation center: http://www.mathworks.com/help/signal/ug/psd-estimate-using-fft.html
The response, 0.5 peak at 100 Hz, seems correct to me, since the theoretical average power of a sinusoid is (A^2)/2. It's also the same answer I get when I type:
mean(x.^2)
My doubt arises when I increase data length, from the code's second line:
t = 0:1/Fs:2-1/Fs;
Why does this change my PSD estimate? Since I'm dealing with a periodic signal, shouldn't the average power remains constant, despite data length?
Thank you, Vinícius

Best Answer

Because the periodogram is strictly a PSD estimate unless you specify the 'power' option. By doubling the time interval you are integrating over twice the interval.
If you specify the 'power' option, you'll get what you expect 0.5
Fs = 1000;
 t = 0:1/Fs:2-1/Fs;
 x = sin(2*pi*100*t);
 [psdestx,Fxx] = periodogram(x,[],length(x),Fs,'power');
 plot(Fxx,psdestx); grid on;
 xlabel('Hz');
 title('Periodogram Power Estimate');
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